Entropy of systems
Keyword(s):
In this paper we show that any ergodic measure preserving transformation of a standard probability space which is $\text{AT}(n)$ for some positive integer $n$ has zero entropy. We show that for every positive integer $n$ any Bernoulli shift is not $\text{AT}(n)$. We also give an example of a transformation which has zero entropy but does not have property $\text{AT}(n)$ for any integer $n\geq 1$.
Keyword(s):
2015 ◽
Vol 36
(7)
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pp. 2172-2202
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1982 ◽
Vol 18
(1)
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pp. 35-48
1999 ◽
Vol 19
(5)
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pp. 1255-1280
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Keyword(s):
2012 ◽
Vol 34
(1)
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pp. 110-131
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1982 ◽
Vol 34
(6)
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pp. 1303-1318
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1983 ◽
Vol 35
(2)
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pp. 339-352
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